Polytope of Type {2,4,15,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,15,6}*1440
if this polytope has a name.
Group : SmallGroup(1440,5900)
Rank : 5
Schlafli Type : {2,4,15,6}
Number of vertices, edges, etc : 2, 4, 30, 45, 6
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,4,15,2}*480
   5-fold quotients : {2,4,3,6}*288
   15-fold quotients : {2,4,3,2}*96
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)(20,22)
(23,25)(24,26)(27,29)(28,30)(31,33)(32,34)(35,37)(36,38)(39,41)(40,42)(43,45)
(44,46)(47,49)(48,50)(51,53)(52,54)(55,57)(56,58)(59,61)(60,62);;
s2 := ( 4, 5)( 7,19)( 8,21)( 9,20)(10,22)(11,15)(12,17)(13,16)(14,18)(23,43)
(24,45)(25,44)(26,46)(27,59)(28,61)(29,60)(30,62)(31,55)(32,57)(33,56)(34,58)
(35,51)(36,53)(37,52)(38,54)(39,47)(40,49)(41,48)(42,50);;
s3 := ( 3,27)( 4,30)( 5,29)( 6,28)( 7,23)( 8,26)( 9,25)(10,24)(11,39)(12,42)
(13,41)(14,40)(15,35)(16,38)(17,37)(18,36)(19,31)(20,34)(21,33)(22,32)(43,47)
(44,50)(45,49)(46,48)(51,59)(52,62)(53,61)(54,60)(56,58);;
s4 := (23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(31,51)(32,52)
(33,53)(34,54)(35,55)(36,56)(37,57)(38,58)(39,59)(40,60)(41,61)(42,62);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s1*s2, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(62)!(1,2);
s1 := Sym(62)!( 3, 5)( 4, 6)( 7, 9)( 8,10)(11,13)(12,14)(15,17)(16,18)(19,21)
(20,22)(23,25)(24,26)(27,29)(28,30)(31,33)(32,34)(35,37)(36,38)(39,41)(40,42)
(43,45)(44,46)(47,49)(48,50)(51,53)(52,54)(55,57)(56,58)(59,61)(60,62);
s2 := Sym(62)!( 4, 5)( 7,19)( 8,21)( 9,20)(10,22)(11,15)(12,17)(13,16)(14,18)
(23,43)(24,45)(25,44)(26,46)(27,59)(28,61)(29,60)(30,62)(31,55)(32,57)(33,56)
(34,58)(35,51)(36,53)(37,52)(38,54)(39,47)(40,49)(41,48)(42,50);
s3 := Sym(62)!( 3,27)( 4,30)( 5,29)( 6,28)( 7,23)( 8,26)( 9,25)(10,24)(11,39)
(12,42)(13,41)(14,40)(15,35)(16,38)(17,37)(18,36)(19,31)(20,34)(21,33)(22,32)
(43,47)(44,50)(45,49)(46,48)(51,59)(52,62)(53,61)(54,60)(56,58);
s4 := Sym(62)!(23,43)(24,44)(25,45)(26,46)(27,47)(28,48)(29,49)(30,50)(31,51)
(32,52)(33,53)(34,54)(35,55)(36,56)(37,57)(38,58)(39,59)(40,60)(41,61)(42,62);
poly := sub<Sym(62)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s1*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope